α -Dissipativity filtering for singular Markovian jump systems with distributed delays

A unified filter for singular Markovian jump systems with mixed delays based on an extended free‐matrix‐based inequality approach

“…16,17 Time delays including discrete delays 18,19 and distributed delays 20,21 are often unavoidable and might cause oscillation, divergence, and even instability for a system. Thus, filtering of SMJSs with discrete or/and distributed delays has become an important topic, and many results have been achieved such as H ∞ filtering, 19,[21][22][23][24] L 2 − L ∞ filtering, 25,26 passive filtering, 27,28 dissipative filtering, 20,29,30 and extended dissipative filtering. 31,32 Note that the extended dissipative filtering is proposed in Reference 33, it simultaneously contains H ∞ filtering, L 2 − L ∞ filtering, passive filtering, and dissipative filtering by tuning some weighting parameters.…”

State bounding estimation for a linear continuous-time singular system with time-varying delay

“…During the past years, state bounding estimation has been widely applied in control systems with actuator saturation, peak-to-peak gain minimization, and parameter estimation (see [1][2][3][4][5]). A state bounding estimation is meant to get the corresponding state bounding set which is limited by the inside and outside of the initial conditions.…”

Mixed filter design for nonlinear singular Markovian jump systems with time-varying delays based on a dissipativity performance index

“…Therefore, not only the stochastic stability but also the regularity and non-impulsiveness (continuous-time) or causality (discrete-time) need to be considered. So far, lots of results have been presented in the literature for the analysis and synthesis of SMJSs (Balasubramaniam et al, 2012; Cui et al, 2016; Liu et al, 2017; Long et al, 2014; Shen et al, 2015a, 2016; Wu et al, 2010a, 2010b; Zhuang et al, 2016b, 2016a).…”

“…Recently, some results on dissipativity analysis for SMJSs have been developed in the literature. For example, in Cui et al (2016), the problem of dissipativity analysis for SMJSs with mode-dependent discrete and distributed delays was dealt with; in Shen et al (2015a), by a mode-dependent stochastic Lyapunov–Krasovskii functional (LKF) and some novel inequalities, less conservative and more general conditions were obtained for SMJSs with constant time delays to be stochastically admissible and satisfy a dissipativity performance; Liu et al (2017) considered the problem of dissipativity filtering for SMJSs with distributed delays, where an integral partitioning technique was used and both mode-dependent and mode-independent filters were designed.…”

“…To mention a few, mode-dependent filters were designed in Wu et al (2010a) and Zhuang et al (2016b, 2016a). Wu et al (2010b) investigated the problem of mode-independent filter design, both mode-dependent filters and mode-independent filters were designed in Zhang et al (2013) and Liu et al (2017), and in Shen et al (2016), a general filter that contains mode-dependent and mode-independent filters in a unified framework was designed for discrete-time SMJSs with time-varying delays. In addition, in practice, the impact of a nonlinear perturbation on a control system cannot be ignored (see Balasubramaniam et al (2012), Krishnasamy and Balasubramaniam (2016), Long et al (2014) and Wang et al (2015) for details).…”